(2)  If \(E\)  is ample, then \(E\)  is Kobayashi positive. 

Not much is known about these two conjectures save for \(n=1\)  by [1]}, [2]} (see recent progress [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}). Note that the converse of each conjecture is true ([9]}, [14]}).
